Hot deformation and associated structural changes were studied in compression of a magnesium alloy AZ31 with initial grain sizes (D0) of 22 µm and 90 µm at a temperature of 573K. D0 influences significantly the flow curve and the kinetics of grain refinement during hot deformation. For D0 = 22 µm, grain fragmentation takes place due to frequent formation of kink bands initially at corrugated grain boundaries and then in grain interiors in low strain, followed by full development of new fine grains in high strain. For D0 = 90 µm, in contrast, twinning takes place in coarser original grains, and then kink bands and new fine grains are formed mainly in finer ones at low strains. Then new grains are formed in necklace along the boundaries of coarse original grains, followed by their development into the grain interiors. Grain refinement in the Mg alloy can be concluded to result from a series of deformation-induced continuous reactions, they are essentially similar to continuous dynamic recrystallization (cDRX).